BesselJZeros(v, n) denotes the n-th positive real root of the BesselJ function of order v.

- If v is numeric, then it must be a real constant. If v is a float, then a numerical evaluation is attempted, otherwise a symbolic representation is returned.

- If n is numeric, then it must be a positive integer.

BesselJZeros(v, n1..n2) represents the sequence of consecutive zeros with index from n1 to n2.

BesselYZeros(v, n) and BesselYZeros(v, n1..n2) correspond to the zeros of the BesselY function.

Note that if $v\ne 0$ then BesselJZeros(v, 0) is also defined and is equal to 0.

These functions may use fsolve to find a floating point approximation for the zeros. To solve ill-conditioned problems, it is convenient to assign the name 'fulldigits' to the environment variable_Envfulldigits.

$\mathrm{BesselJZeros}\left(0\,1\right)$

$\mathrm{BesselJZeros}\left(0\,1\right)$

$\mathrm{evalf}\left(\mathrm{BesselJZeros}\left(0\,1\right)\right)$

$2.404825558$

$\mathrm{BesselJZeros}\left(1.5\,10\right)$

$32.95638904$

$\mathrm{BesselJZeros}\left(\frac{1}{2}\,5\right)$

$5\mathrm{\pi }$

$\mathrm{BesselYZeros}\left(\frac{1}{2}\,5\right)$

$\frac{9\mathrm{\pi }}{2}$

$\mathrm{BesselJZeros}\left(1\,0\right)$

$0$

$\mathrm{BesselJZeros}\left(1.\,3..6\right)$

$10.17346814,13.32369194,16.47063005,19.61585851$

$s≔\mathrm{BesselYZeros}\left(1\,3..6\right)$

$s≔\mathrm{BesselYZeros}\left(1\,3..6\right)$

$\mathrm{evalf}\left(s\right)$

$8.596005868,11.74915483,14.89744213,18.04340228$

$\mathrm{BesselJ}\left(v\,\mathrm{BesselJZeros}\left(v\,3\right)\right)$

$0$